REGRESSION Flashcards
statistical technique for finding the best-fitting straight line for
a set of data
regression
the best-fitting straight line for
a set of data or resulting straight line is
called
regression line
Y=bX+a
Linear Equation
Y=bX+a
Regression Equation
Y=bX+a what is the slope
b
determines how much the Y variable changes when X is
increased by one point.
slope (b)
Y=bX+a The value of a in the general equation is called
Y-intercept
it determines the value of Y when X = 0
a or the Y-intercept
(Y=bX+a)
On a graph, the _ value identifies the point where the line intercepts the Y-axis
a (Y=bX+a)
means that Y increases when X is increased, what slope
positive slope
indicates that Y decreases when X is increased, what slope
negative slope
regression equation for Y is the _ equation
linear equation
distance between the actual data point (Y) and the predicted point on the line (Ŷ) is defined as
formula:
Y – Ŷ
The Regression Equation for Prediction
Ŷ =
Ŷ = bX + a
The goal of _ is to find the equation for the line that minimizes these (Y – Ŷ) distances.
regression
gives a measure of the standard distance between the predicted Y values on the regression line and the actual Y values in the data.
standard error of estimate
process of testing the significance of a regression equation and is very similar to the analysis of variance (ANOVA)
analysis of
analysis of regression
The variability for the original Y scores (both SS and df) is partitioned into _
components
TWO
(1) the variability that is predicted by the regression
equation and
(2) the residual variability
two components of variability for the original Y scores
(1) the variability that is predicted by the regression equation
components of variability for the original Y scores
(2) the residual variability
components of variability for the original Y scores
The slope of the regression equation (b or beta) is zero. what hypotheses in analysis of regression?
Ho
The slope of the regression equation (b or beta) is not zero. what hypotheses in analysis of regression?
H1
Variable X significantly predicts variable Y. what hypotheses in analysis of regression?
H1
process of using several predictor variables to help obtain
more accurate predictions.
Multiple Regression
different _ variables are related to each other, which means that they are often measuring and predicting the same thing.
predictor variables
Is adding more variables to the equation always better?
no
the variables may _ with each other, adding another predictor variable to a regression equation does not always add to the accuracy of prediction.
variables may overlap with each other
Regression Equations with Two Predictors
Multiple Regression
Ŷ = b₁X₁ + b₂x₂ + a
Regression Equations with Two Predictors/Multiple Regression
describes the proportion of the total variability of the Y scores that is accounted for by the regression equation.
R²
can be defined as the standard distance between the predicted Y values (from the regression equation) and the actual Y values (in the data)
standard error of
estimate
use to determine whether the equation predicts a significant portion of the variance for the Y scores.
F-ratio
determines the value of Y when X = 0
a = Constant or the Y-intercept
_ analysis evaluates the contribution of each predictor variable after the influence of the other predictor has been considered.
regression analysis
(Partial Correlations (β))
you can determine whether each predictor variable contributes to the relationship by itself or simply duplicates the contribution already made by another variable.
Partial Correlations (β) (regression analysis)
R², F value (F), degrees of freedom (numerator, denominator; in parentheses separated by a comma next to F), and significance level (p), β. Report the β and the corresponding t-test for that predictors for each predictor in the regression. (R²=.358, F(2,55)=5.56, p<.01). (β = .56, p<.001), as did agreeableness ((β= -.36, p<.01).
Reporting Results Regression
_ table presents the analysis of regression evaluating the significance of the regression equation, including the F-ratio and the level of significance (the p value or alpha level for the test).
ANOVA TABLE
summarizes the unstandardized and the standardized coefficients for the regression equation.
_ table
Coefficients table
The standardized coefficients are the _ values
beta (b) values.
For one predictor, beta is simply
the _ correlation between X and Y.
Pearson Correlation
the table uses a _ statistic to evaluate the significance of each predictor variable. For one predictor variable, this is identical to the significance of the regression equation and you should find that t is equal to the square root of the F-ratio from the analysis of regression.
t statistic
For two predictor variables, the t values measure the _ of the contribution of each variable beyond what is already predicted by the other variable.
significance
On a graph, it identifies the point where the line intercepts the Y-axis
Y-intercept/Constant
is the actual data point
Y
the predicted point on the line
(the straight line)
Ŷ (Y hat)
each data point is an _ of X and Y
intersection
actual data point may be _ from the computed regression equation
different
perfect correlation
correlation is r = +1.00
